harmonic

harmonic.

1 Physical term describing the vibration in segments of a sound-producing body (see sound). A string vibrates simultaneously in its whole length and in segments of halves, thirds, fourths, etc. These segments form what is known in algebra as a harmonic series or progression, since the rate of vibration of each segment is an integral multiple of the frequency of the whole string, i.e., each segment vibrates respectively twice, three times, four times, etc., as fast as the whole string. The vibration of the whole string produces the fundamental tone, and the segments produce weaker subsidiary tones. A similar phenomenon occurs in an air column in a pipe. At most the first 16 tones in such a series can be heard by the human ear; the character or timbre of a fundamental tone is determined by the number of its subsidiary tones heard and their relative intensity. The subsidiary tones have been loosely called harmonics (as a noun), but they are properly called partials, the fundamental tone being the first partial. They are also called overtones (a synonym for "upper partials"), although this term includes a number of sounds that do not fit in with the harmonic series, and are therefore not considered musical. 2 Term describing the silvery sound produced separately when the fundamental and possibly more partial tones are damped by touching a string at a nodal point. Similarly harmonics are produced separately in an air column by overblowing or in brass wind instruments by the use of valves.

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Harmonic (periodic phenomena)

A sinusoidal quantity having a frequency that is an integral multiple of the frequency of a periodic quantity to which it is related. See Mode of vibration

A harmonic series of sounds is one in which the basic frequency of each sound is an integral multiple of some fundamental frequency. The name exists for historical reasons, even though according to the usual mathematical definition such frequencies form an arithmetic series. An ideal string (or air column) can vibrate as a whole or in a number of equal parts, and the respective periods of vibration are proportional to the lengths. These increasingly shorter lengths or periods form a harmonic series. The name came from the harmonious relation of such sounds, and the science of musical acoustics was once called harmonics. Nowadays, it is customary to deal with ratios of frequency rather than ratios of length and, because frequency is the reciprocal of period, the definition of harmonic in acoustics becomes that given here. See Musical acoustics

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

harmonic

[här′män·ik]

(acoustics)

One of a series of sounds, each of which has a frequency which is an integral multiple of some fundamental frequency.

(mathematics)

A solution of Laplace's equation which is separable in a specified coordinate system.

(physics)

A sinusoidal component of a periodic wave, having a frequency that is an integral multiple of the fundamental frequency. Also known as harmonic component.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

harmonic

A component of a sound containing more than one frequency which is an integral multiple of the lowest frequency.

McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.

harmonic

A vibration whose frequency is an even multiple of another vibration or fundamental frequency. The first harmonic of a 200-Hz vibration has a frequency of 200 Hz. This is also its fundamental frequency. The second harmonic will have a frequency of 400 Hz, the third 800 Hz, the fourth 1600 Hz, and so on.

An Illustrated Dictionary of Aviation Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved

harmonic

1. Music of, relating to, or belonging to harmony

2. Maths

a. capable of expression in the form of sine and cosine functions

b. of or relating to numbers whose reciprocals form an arithmetic progression

3. Physics of or concerned with an oscillation that has a frequency that is an integral multiple of a fundamental frequency

4. Physics Music a component of a periodic quantity, such as a musical tone, with a frequency that is an integral multiple of the fundamental frequency. The first harmonic is the fundamental, the second harmonic (twice the fundamental frequency) is the first overtone, the third harmonic (three times the fundamental frequency) is the second overtone, etc.

5. Music (not in technical use) overtone: in this case, the first overtone is the first harmonic, etc.

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

harmonic

A multiple of a fundamental frequency occurring at the same time. For example, if the fundamental frequency is 1 kHz, the first harmonic is 1 kHz, the second harmonic is 2 kHz, and so on. Musical instruments oscillate at several frequencies, which are called "overtones." The first overtone is actually the second harmonic, and so on. See harmonic distortion.

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